LMFDB - Embedded newform 975.2.c.j.274.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(274,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5089536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 16x^2 - 24*x + 18
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.3
Root			$-1.33641 - 1.33641i$ of defining polynomial
Character	$\chi$	$=$	975.274
Dual form			975.2.c.j.274.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.571993i q^{2} +1.00000i q^{3} +1.67282 q^{4} +0.571993 q^{6} -1.42801i q^{7} -2.10083i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.571993i q^{2} +1.00000i q^{3} +1.67282 q^{4} +0.571993 q^{6} -1.42801i q^{7} -2.10083i q^{8} -1.00000 q^{9} +3.24482 q^{11} +1.67282i q^{12} +1.00000i q^{13} -0.816810 q^{14} +2.14399 q^{16} -1.85601i q^{17} +0.571993i q^{18} +1.81681 q^{19} +1.42801 q^{21} -1.85601i q^{22} -1.52884i q^{23} +2.10083 q^{24} +0.571993 q^{26} -1.00000i q^{27} -2.38880i q^{28} -2.34565 q^{29} +6.38880 q^{31} -5.42801i q^{32} +3.24482i q^{33} -1.06163 q^{34} -1.67282 q^{36} -3.52884i q^{37} -1.03920i q^{38} -1.00000 q^{39} -3.81681 q^{41} -0.816810i q^{42} +10.0185i q^{43} +5.42801 q^{44} -0.874485 q^{46} -11.2633i q^{47} +2.14399i q^{48} +4.96080 q^{49} +1.85601 q^{51} +1.67282i q^{52} +6.81681i q^{53} -0.571993 q^{54} -3.00000 q^{56} +1.81681i q^{57} +1.34169i q^{58} +5.91764 q^{59} +5.48963 q^{61} -3.65435i q^{62} +1.42801i q^{63} +1.18319 q^{64} +1.85601 q^{66} +10.3025i q^{67} -3.10478i q^{68} +1.52884 q^{69} -9.81681 q^{71} +2.10083i q^{72} +5.32718i q^{73} -2.01847 q^{74} +3.03920 q^{76} -4.63362i q^{77} +0.571993i q^{78} +2.96080 q^{79} +1.00000 q^{81} +2.18319i q^{82} +3.14003i q^{83} +2.38880 q^{84} +5.73050 q^{86} -2.34565i q^{87} -6.81681i q^{88} +4.85601 q^{89} +1.42801 q^{91} -2.55748i q^{92} +6.38880i q^{93} -6.44252 q^{94} +5.42801 q^{96} -1.51037i q^{97} -2.83754i q^{98} -3.24482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 2 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 2 q^{6} - 6 q^{9} - 2 q^{11} + 18 q^{14} + 10 q^{16} - 12 q^{19} + 10 q^{21} - 6 q^{24} + 2 q^{26} + 26 q^{29} + 14 q^{31} + 38 q^{34} + 10 q^{36} - 6 q^{39} + 34 q^{44} + 52 q^{46} + 4 q^{49} + 14 q^{51} - 2 q^{54} - 18 q^{56} - 6 q^{59} - 10 q^{61} + 30 q^{64} + 14 q^{66} - 8 q^{69} - 36 q^{71} + 48 q^{74} + 44 q^{76} - 8 q^{79} + 6 q^{81} - 10 q^{84} - 20 q^{86} + 32 q^{89} + 10 q^{91} + 10 q^{94} + 34 q^{96} + 2 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^6 - 6 * q^9 - 2 * q^11 + 18 * q^14 + 10 * q^16 - 12 * q^19 + 10 * q^21 - 6 * q^24 + 2 * q^26 + 26 * q^29 + 14 * q^31 + 38 * q^34 + 10 * q^36 - 6 * q^39 + 34 * q^44 + 52 * q^46 + 4 * q^49 + 14 * q^51 - 2 * q^54 - 18 * q^56 - 6 * q^59 - 10 * q^61 + 30 * q^64 + 14 * q^66 - 8 * q^69 - 36 * q^71 + 48 * q^74 + 44 * q^76 - 8 * q^79 + 6 * q^81 - 10 * q^84 - 20 * q^86 + 32 * q^89 + 10 * q^91 + 10 * q^94 + 34 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 0.571993i	− 0.404460i	−0.979338	−	0.202230i	$-0.935181\pi$
$2$	− 0.571993i	− 0.404460i	0.979338	−	0.202230i	$-0.0648189\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.67282	0.836412
$5$	0	0
$5$	0	0
$6$	0.571993	0.233515
$7$	− 1.42801i	− 0.539736i	−0.962897	−	0.269868i	$-0.913020\pi$
$7$	− 1.42801i	− 0.539736i	0.962897	−	0.269868i	$-0.0869800\pi$
$8$	− 2.10083i	− 0.742756i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	3.24482	0.978349	0.489175	−	0.872186i	$-0.337298\pi$
$11$	3.24482	0.978349	0.489175	+	0.872186i	$0.337298\pi$
$12$	1.67282i	0.482903i
$13$	1.00000i	0.277350i
$13$	1.00000i	0.277350i
$14$	−0.816810	−0.218302
$15$	0	0
$16$	2.14399	0.535997
$17$	− 1.85601i	− 0.450149i	−0.974342	−	0.225075i	$-0.927737\pi$
$17$	− 1.85601i	− 0.450149i	0.974342	−	0.225075i	$-0.0722626\pi$
$18$	0.571993i	0.134820i
$19$	1.81681	0.416805	0.208402	−	0.978043i	$-0.433174\pi$
$19$	1.81681	0.416805	0.208402	+	0.978043i	$0.433174\pi$
$20$	0	0
$21$	1.42801	0.311617
$22$	− 1.85601i	− 0.395703i
$23$	− 1.52884i	− 0.318785i	−0.987215	−	0.159392i	$-0.949047\pi$
$23$	− 1.52884i	− 0.318785i	0.987215	−	0.159392i	$-0.0509535\pi$
$24$	2.10083	0.428830
$25$	0	0
$26$	0.571993	0.112177
$27$	− 1.00000i	− 0.192450i
$28$	− 2.38880i	− 0.451441i
$29$	−2.34565	−0.435576	−0.217788	−	0.975996i	$-0.569884\pi$
$29$	−2.34565	−0.435576	−0.217788	+	0.975996i	$0.569884\pi$
$30$	0	0
$31$	6.38880	1.14746	0.573731	−	0.819043i	$-0.305495\pi$
$31$	6.38880	1.14746	0.573731	+	0.819043i	$0.305495\pi$
$32$	− 5.42801i	− 0.959545i
$33$	3.24482i	0.564850i
$34$	−1.06163	−0.182068
$35$	0	0
$36$	−1.67282	−0.278804
$37$	− 3.52884i	− 0.580137i	−0.957006	−	0.290069i	$-0.906322\pi$
$37$	− 3.52884i	− 0.580137i	0.957006	−	0.290069i	$-0.0936781\pi$
$38$	− 1.03920i	− 0.168581i
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−3.81681	−0.596086	−0.298043	−	0.954553i	$-0.596334\pi$
$41$	−3.81681	−0.596086	−0.298043	+	0.954553i	$0.596334\pi$
$42$	− 0.816810i	− 0.126037i
$43$	10.0185i	1.52780i	0.645333	+	0.763901i	$0.276719\pi$
$43$	10.0185i	1.52780i	−0.645333	+	0.763901i	$0.723281\pi$
$44$	5.42801	0.818303
$45$	0	0
$46$	−0.874485	−0.128936
$47$	− 11.2633i	− 1.64292i	−0.570267	−	0.821460i	$-0.693160\pi$
$47$	− 11.2633i	− 1.64292i	0.570267	−	0.821460i	$-0.306840\pi$
$48$	2.14399i	0.309458i
$49$	4.96080	0.708685
$50$	0	0
$51$	1.85601	0.259894
$52$	1.67282i	0.231979i
$53$	6.81681i	0.936361i	0.883633	+	0.468180i	$0.155090\pi$
$53$	6.81681i	0.936361i	−0.883633	+	0.468180i	$0.844910\pi$
$54$	−0.571993	−0.0778384
$55$	0	0
$56$	−3.00000	−0.400892
$57$	1.81681i	0.240642i
$58$	1.34169i	0.176173i
$59$	5.91764	0.770411	0.385206	−	0.922831i	$-0.374131\pi$
$59$	5.91764	0.770411	0.385206	+	0.922831i	$0.374131\pi$
$60$	0	0
$61$	5.48963	0.702876	0.351438	−	0.936211i	$-0.385693\pi$
$61$	5.48963	0.702876	0.351438	+	0.936211i	$0.385693\pi$
$62$	− 3.65435i	− 0.464103i
$63$	1.42801i	0.179912i
$64$	1.18319	0.147899
$65$	0	0
$66$	1.85601	0.228459
$67$	10.3025i	1.25865i	0.777142	+	0.629325i	$0.216668\pi$
$67$	10.3025i	1.25865i	−0.777142	+	0.629325i	$0.783332\pi$
$68$	− 3.10478i	− 0.376510i
$69$	1.52884	0.184050
$70$	0	0
$71$	−9.81681	−1.16504	−0.582521	−	0.812816i	$-0.697933\pi$
$71$	−9.81681	−1.16504	−0.582521	+	0.812816i	$0.697933\pi$
$72$	2.10083i	0.247585i
$73$	5.32718i	0.623499i	0.950164	+	0.311749i	$0.100915\pi$
$73$	5.32718i	0.623499i	−0.950164	+	0.311749i	$0.899085\pi$
$74$	−2.01847	−0.234642
$75$	0	0
$76$	3.03920	0.348621
$77$	− 4.63362i	− 0.528050i
$78$	0.571993i	0.0647655i
$79$	2.96080	0.333116	0.166558	−	0.986032i	$-0.446735\pi$
$79$	2.96080	0.333116	0.166558	+	0.986032i	$0.446735\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.18319i	0.241093i
$83$	3.14003i	0.344663i	0.985039	+	0.172332i	$0.0551301\pi$
$83$	3.14003i	0.344663i	−0.985039	+	0.172332i	$0.944870\pi$
$84$	2.38880	0.260640
$85$	0	0
$86$	5.73050	0.617935
$87$	− 2.34565i	− 0.251480i
$88$	− 6.81681i	− 0.726674i
$89$	4.85601	0.514736	0.257368	−	0.966313i	$-0.417145\pi$
$89$	4.85601	0.514736	0.257368	+	0.966313i	$0.417145\pi$
$90$	0	0
$91$	1.42801	0.149696
$92$	− 2.55748i	− 0.266635i
$93$	6.38880i	0.662488i
$94$	−6.44252	−0.664496
$95$	0	0
$96$	5.42801	0.553994
$97$	− 1.51037i	− 0.153354i	−0.997056	−	0.0766772i	$-0.975569\pi$
$97$	− 1.51037i	− 0.153354i	0.997056	−	0.0766772i	$-0.0244311\pi$
$98$	− 2.83754i	− 0.286635i
$99$	−3.24482	−0.326116
$100$	0	0
$101$	−17.0185	−1.69340	−0.846701	−	0.532070i	$-0.821414\pi$
$101$	−17.0185	−1.69340	−0.846701	+	0.532070i	$0.821414\pi$
$102$	− 1.06163i	− 0.105117i
$103$	− 9.73050i	− 0.958774i	−0.877603	−	0.479387i	$-0.840859\pi$
$103$	− 9.73050i	− 0.958774i	0.877603	−	0.479387i	$-0.159141\pi$
$104$	2.10083	0.206003
$105$	0	0
$106$	3.89917	0.378721
$107$	3.43196i	0.331780i	0.986144	+	0.165890i	$0.0530497\pi$
$107$	3.43196i	0.331780i	−0.986144	+	0.165890i	$0.946950\pi$
$108$	− 1.67282i	− 0.160968i
$109$	2.96080	0.283593	0.141796	−	0.989896i	$-0.454712\pi$
$109$	2.96080	0.283593	0.141796	+	0.989896i	$0.454712\pi$
$110$	0	0
$111$	3.52884	0.334942
$112$	− 3.06163i	− 0.289297i
$113$	− 9.54731i	− 0.898135i	−0.893498	−	0.449068i	$-0.851756\pi$
$113$	− 9.54731i	− 0.898135i	0.893498	−	0.449068i	$-0.148244\pi$
$114$	1.03920	0.0973303
$115$	0	0
$116$	−3.92385	−0.364321
$117$	− 1.00000i	− 0.0924500i
$118$	− 3.38485i	− 0.311601i
$119$	−2.65040	−0.242962
$120$	0	0
$121$	−0.471163	−0.0428330
$122$	− 3.14003i	− 0.284285i
$123$	− 3.81681i	− 0.344150i
$124$	10.6873	0.959752
$125$	0	0
$126$	0.816810	0.0727672
$127$	0.183190i	0.0162555i	0.999967	+	0.00812773i	$0.00258717\pi$
$127$	0.183190i	0.0162555i	−0.999967	+	0.00812773i	$0.997413\pi$
$128$	− 11.5328i	− 1.01936i
$129$	−10.0185	−0.882077
$130$	0	0
$131$	−17.4504	−1.52465	−0.762326	−	0.647194i	$-0.775942\pi$
$131$	−17.4504	−1.52465	−0.762326	+	0.647194i	$0.775942\pi$
$132$	5.42801i	0.472447i
$133$	− 2.59442i	− 0.224965i
$134$	5.89296	0.509074
$135$	0	0
$136$	−3.89917	−0.334351
$137$	− 1.79834i	− 0.153642i	−0.997045	−	0.0768212i	$-0.975523\pi$
$137$	− 1.79834i	− 0.153642i	0.997045	−	0.0768212i	$-0.0244771\pi$
$138$	− 0.874485i	− 0.0744411i
$139$	−20.3249	−1.72394	−0.861968	−	0.506962i	$-0.830768\pi$
$139$	−20.3249	−1.72394	−0.861968	+	0.506962i	$0.830768\pi$
$140$	0	0
$141$	11.2633	0.948540
$142$	5.61515i	0.471213i
$143$	3.24482i	0.271345i
$144$	−2.14399	−0.178666
$145$	0	0
$146$	3.04711	0.252181
$147$	4.96080i	0.409160i
$148$	− 5.90312i	− 0.485234i
$149$	17.1809	1.40752	0.703758	−	0.710440i	$-0.251504\pi$
$149$	17.1809	1.40752	0.703758	+	0.710440i	$0.251504\pi$
$150$	0	0
$151$	3.99605	0.325194	0.162597	−	0.986693i	$-0.448013\pi$
$151$	3.99605	0.325194	0.162597	+	0.986693i	$0.448013\pi$
$152$	− 3.81681i	− 0.309584i
$153$	1.85601i	0.150050i
$154$	−2.65040	−0.213575
$155$	0	0
$156$	−1.67282	−0.133933
$157$	− 7.67282i	− 0.612358i	−0.951974	−	0.306179i	$-0.900949\pi$
$157$	− 7.67282i	− 0.612358i	0.951974	−	0.306179i	$-0.0990506\pi$
$158$	− 1.69356i	− 0.134732i
$159$	−6.81681	−0.540608
$160$	0	0
$161$	−2.18319	−0.172059
$162$	− 0.571993i	− 0.0449400i
$163$	0.471163i	0.0369043i	0.999830	+	0.0184522i	$0.00587384\pi$
$163$	0.471163i	0.0369043i	−0.999830	+	0.0184522i	$0.994126\pi$
$164$	−6.38485	−0.498573
$165$	0	0
$166$	1.79608	0.139403
$167$	18.7098i	1.44781i	0.689902	+	0.723903i	$0.257654\pi$
$167$	18.7098i	1.44781i	−0.689902	+	0.723903i	$0.742346\pi$
$168$	− 3.00000i	− 0.231455i
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	−1.81681	−0.138935
$172$	16.7591i	1.27787i
$173$	7.96080i	0.605248i	0.953110	+	0.302624i	$0.0978627\pi$
$173$	7.96080i	0.605248i	−0.953110	+	0.302624i	$0.902137\pi$
$174$	−1.34169	−0.101714
$175$	0	0
$176$	6.95684	0.524392
$177$	5.91764i	0.444797i
$178$	− 2.77761i	− 0.208190i
$179$	−15.6521	−1.16989	−0.584946	−	0.811072i	$-0.698884\pi$
$179$	−15.6521	−1.16989	−0.584946	+	0.811072i	$0.698884\pi$
$180$	0	0
$181$	−24.5658	−1.82596	−0.912980	−	0.408004i	$-0.866225\pi$
$181$	−24.5658	−1.82596	−0.912980	+	0.408004i	$0.866225\pi$
$182$	− 0.816810i	− 0.0605460i
$183$	5.48963i	0.405805i
$184$	−3.21183	−0.236779
$185$	0	0
$186$	3.65435	0.267950
$187$	− 6.02242i	− 0.440403i
$188$	− 18.8415i	− 1.37416i
$189$	−1.42801	−0.103872
$190$	0	0
$191$	−21.0577	−1.52368	−0.761840	−	0.647765i	$-0.775704\pi$
$191$	−21.0577	−1.52368	−0.761840	+	0.647765i	$0.775704\pi$
$192$	1.18319i	0.0853894i
$193$	19.9401i	1.43532i	0.696395	+	0.717659i	$0.254786\pi$
$193$	19.9401i	1.43532i	−0.696395	+	0.717659i	$0.745214\pi$
$194$	−0.863919	−0.0620258
$195$	0	0
$196$	8.29854	0.592753
$197$	23.4504i	1.67077i	0.549662	+	0.835387i	$0.314756\pi$
$197$	23.4504i	1.67077i	−0.549662	+	0.835387i	$0.685244\pi$
$198$	1.85601i	0.131901i
$199$	−16.2880	−1.15462	−0.577312	−	0.816524i	$-0.695898\pi$
$199$	−16.2880	−1.15462	−0.577312	+	0.816524i	$0.695898\pi$
$200$	0	0
$201$	−10.3025	−0.726682
$202$	9.73445i	0.684914i
$203$	3.34960i	0.235096i
$204$	3.10478	0.217378
$205$	0	0
$206$	−5.56578	−0.387786
$207$	1.52884i	0.106262i
$208$	2.14399i	0.148659i
$209$	5.89522	0.407781
$210$	0	0
$211$	27.8538	1.91753	0.958766	−	0.284198i	$-0.0917272\pi$
$211$	27.8538	1.91753	0.958766	+	0.284198i	$0.0917272\pi$
$212$	11.4033i	0.783183i
$213$	− 9.81681i	− 0.672637i
$214$	1.96306	0.134192
$215$	0	0
$216$	−2.10083	−0.142943
$217$	− 9.12325i	− 0.619327i
$218$	− 1.69356i	− 0.114702i
$219$	−5.32718	−0.359977
$220$	0	0
$221$	1.85601	0.124849
$222$	− 2.01847i	− 0.135471i
$223$	11.1625i	0.747493i	0.927531	+	0.373747i	$0.121927\pi$
$223$	11.1625i	0.747493i	−0.927531	+	0.373747i	$0.878073\pi$
$224$	−7.75123	−0.517901
$225$	0	0
$226$	−5.46100	−0.363260
$227$	− 7.93611i	− 0.526738i	−0.964695	−	0.263369i	$-0.915166\pi$
$227$	− 7.93611i	− 0.526738i	0.964695	−	0.263369i	$-0.0848337\pi$
$228$	3.03920i	0.201276i
$229$	−27.9585	−1.84755	−0.923776	−	0.382933i	$-0.874914\pi$
$229$	−27.9585	−1.84755	−0.923776	+	0.382933i	$0.874914\pi$
$230$	0	0
$231$	4.63362	0.304870
$232$	4.92781i	0.323526i
$233$	− 1.14399i	− 0.0749450i	−0.999298	−	0.0374725i	$-0.988069\pi$
$233$	− 1.14399i	− 0.0749450i	0.999298	−	0.0374725i	$-0.0119307\pi$
$234$	−0.571993	−0.0373924
$235$	0	0
$236$	9.89917	0.644381
$237$	2.96080i	0.192324i
$238$	1.51601i	0.0982684i
$239$	3.34960	0.216668	0.108334	−	0.994115i	$-0.465448\pi$
$239$	3.34960	0.216668	0.108334	+	0.994115i	$0.465448\pi$
$240$	0	0
$241$	−8.09688	−0.521566	−0.260783	−	0.965397i	$-0.583981\pi$
$241$	−8.09688	−0.521566	−0.260783	+	0.965397i	$0.583981\pi$
$242$	0.269502i	0.0173242i
$243$	1.00000i	0.0641500i
$244$	9.18319	0.587893
$245$	0	0
$246$	−2.18319	−0.139195
$247$	1.81681i	0.115601i
$248$	− 13.4218i	− 0.852285i
$249$	−3.14003	−0.198992
$250$	0	0
$251$	−25.3641	−1.60097	−0.800484	−	0.599353i	$-0.795424\pi$
$251$	−25.3641	−1.60097	−0.800484	+	0.599353i	$0.795424\pi$
$252$	2.38880i	0.150480i
$253$	− 4.96080i	− 0.311883i
$254$	0.104783	0.00657469
$255$	0	0
$256$	−4.23030	−0.264394
$257$	− 19.5865i	− 1.22177i	−0.791718	−	0.610887i	$-0.790813\pi$
$257$	− 19.5865i	− 1.22177i	0.791718	−	0.610887i	$-0.209187\pi$
$258$	5.73050i	0.356765i
$259$	−5.03920	−0.313121
$260$	0	0
$261$	2.34565	0.145192
$262$	9.98153i	0.616661i
$263$	− 7.24877i	− 0.446978i	−0.974706	−	0.223489i	$-0.928255\pi$
$263$	− 7.24877i	− 0.446978i	0.974706	−	0.223489i	$-0.0717447\pi$
$264$	6.81681	0.419546
$265$	0	0
$266$	−1.48399	−0.0909892
$267$	4.85601i	0.297183i
$268$	17.2343i	1.05275i
$269$	14.5104	0.884713	0.442356	−	0.896839i	$-0.354143\pi$
$269$	14.5104	0.884713	0.442356	+	0.896839i	$0.354143\pi$
$270$	0	0
$271$	−4.19771	−0.254993	−0.127496	−	0.991839i	$-0.540694\pi$
$271$	−4.19771	−0.254993	−0.127496	+	0.991839i	$0.540694\pi$
$272$	− 3.97927i	− 0.241279i
$273$	1.42801i	0.0864269i
$274$	−1.02864	−0.0621423
$275$	0	0
$276$	2.55748	0.153942
$277$	16.6050i	0.997697i	0.866689	+	0.498848i	$0.166244\pi$
$277$	16.6050i	0.997697i	−0.866689	+	0.498848i	$0.833756\pi$
$278$	11.6257i	0.697264i
$279$	−6.38880	−0.382488
$280$	0	0
$281$	24.3249	1.45110	0.725551	−	0.688168i	$-0.241585\pi$
$281$	24.3249	1.45110	0.725551	+	0.688168i	$0.241585\pi$
$282$	− 6.44252i	− 0.383647i
$283$	− 7.71203i	− 0.458432i	−0.973376	−	0.229216i	$-0.926384\pi$
$283$	− 7.71203i	− 0.458432i	0.973376	−	0.229216i	$-0.0736163\pi$
$284$	−16.4218	−0.974454
$285$	0	0
$286$	1.85601	0.109748
$287$	5.45043i	0.321729i
$288$	5.42801i	0.319848i
$289$	13.5552	0.797366
$290$	0	0
$291$	1.51037	0.0885392
$292$	8.91143i	0.521502i
$293$	6.00000i	0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$	6.00000i	0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	2.83754	0.165489
$295$	0	0
$296$	−7.41349	−0.430900
$297$	− 3.24482i	− 0.188283i
$298$	− 9.82738i	− 0.569285i
$299$	1.52884	0.0884149
$300$	0	0
$301$	14.3064	0.824610
$302$	− 2.28571i	− 0.131528i
$303$	− 17.0185i	− 0.977686i
$304$	3.89522	0.223406
$305$	0	0
$306$	1.06163	0.0606892
$307$	12.7882i	0.729860i	0.931035	+	0.364930i	$0.118907\pi$
$307$	12.7882i	0.729860i	−0.931035	+	0.364930i	$0.881093\pi$
$308$	− 7.75123i	− 0.441667i
$309$	9.73050	0.553549
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	2.10083i	0.118936i
$313$	13.8824i	0.784679i	0.919820	+	0.392340i	$0.128334\pi$
$313$	13.8824i	0.784679i	−0.919820	+	0.392340i	$0.871666\pi$
$314$	−4.38880	−0.247675
$315$	0	0
$316$	4.95289	0.278622
$317$	− 8.01847i	− 0.450362i	−0.974317	−	0.225181i	$-0.927703\pi$
$317$	− 8.01847i	− 0.450362i	0.974317	−	0.225181i	$-0.0722974\pi$
$318$	3.89917i	0.218655i
$319$	−7.61120	−0.426145
$320$	0	0
$321$	−3.43196	−0.191553
$322$	1.24877i	0.0695912i
$323$	− 3.37202i	− 0.187624i
$324$	1.67282	0.0929347
$325$	0	0
$326$	0.269502	0.0149263
$327$	2.96080i	0.163732i
$328$	8.01847i	0.442746i
$329$	−16.0841	−0.886742
$330$	0	0
$331$	−34.2201	−1.88091	−0.940454	−	0.339920i	$-0.889600\pi$
$331$	−34.2201	−1.88091	−0.940454	+	0.339920i	$0.889600\pi$
$332$	5.25272i	0.288281i
$333$	3.52884i	0.193379i
$334$	10.7019	0.585580
$335$	0	0
$336$	3.06163	0.167025
$337$	− 21.4712i	− 1.16961i	−0.811174	−	0.584804i	$-0.801171\pi$
$337$	− 21.4712i	− 1.16961i	0.811174	−	0.584804i	$-0.198829\pi$
$338$	0.571993i	0.0311123i
$339$	9.54731	0.518539
$340$	0	0
$341$	20.7305	1.12262
$342$	1.03920i	0.0561937i
$343$	− 17.0801i	− 0.922239i
$344$	21.0471	1.13478
$345$	0	0
$346$	4.55352	0.244799
$347$	26.6129i	1.42865i	0.699812	+	0.714327i	$0.253267\pi$
$347$	26.6129i	1.42865i	−0.699812	+	0.714327i	$0.746733\pi$
$348$	− 3.92385i	− 0.210341i
$349$	13.8168	0.739597	0.369798	−	0.929112i	$-0.379427\pi$
$349$	13.8168	0.739597	0.369798	+	0.929112i	$0.379427\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	− 17.6129i	− 0.938770i
$353$	25.5288i	1.35876i	0.733785	+	0.679381i	$0.237752\pi$
$353$	25.5288i	1.35876i	−0.733785	+	0.679381i	$0.762248\pi$
$354$	3.38485	0.179903
$355$	0	0
$356$	8.12325	0.430532
$357$	− 2.65040i	− 0.140274i
$358$	8.95289i	0.473175i
$359$	−4.65831	−0.245856	−0.122928	−	0.992416i	$-0.539228\pi$
$359$	−4.65831	−0.245856	−0.122928	+	0.992416i	$0.539228\pi$
$360$	0	0
$361$	−15.6992	−0.826274
$362$	14.0515i	0.738528i
$363$	− 0.471163i	− 0.0247296i
$364$	2.38880	0.125207
$365$	0	0
$366$	3.14003	0.164132
$367$	19.2672i	1.00574i	0.864362	+	0.502871i	$0.167723\pi$
$367$	19.2672i	1.00574i	−0.864362	+	0.502871i	$0.832277\pi$
$368$	− 3.27781i	− 0.170867i
$369$	3.81681	0.198695
$370$	0	0
$371$	9.73445	0.505388
$372$	10.6873i	0.554113i
$373$	− 6.12552i	− 0.317167i	−0.987346	−	0.158584i	$-0.949307\pi$
$373$	− 6.12552i	− 0.317167i	0.987346	−	0.158584i	$-0.0506927\pi$
$374$	−3.44479	−0.178126
$375$	0	0
$376$	−23.6623	−1.22029
$377$	− 2.34565i	− 0.120807i
$378$	0.816810i	0.0420122i
$379$	−22.3104	−1.14601	−0.573004	−	0.819553i	$-0.694222\pi$
$379$	−22.3104	−1.14601	−0.573004	+	0.819553i	$0.694222\pi$
$380$	0	0
$381$	−0.183190	−0.00938510
$382$	12.0448i	0.616268i
$383$	− 37.0841i	− 1.89491i	−0.319894	−	0.947453i	$-0.603647\pi$
$383$	− 37.0841i	− 1.89491i	0.319894	−	0.947453i	$-0.396353\pi$
$384$	11.5328	0.588530
$385$	0	0
$386$	11.4056	0.580529
$387$	− 10.0185i	− 0.509268i
$388$	− 2.52658i	− 0.128267i
$389$	23.8353	1.20850	0.604248	−	0.796796i	$-0.293473\pi$
$389$	23.8353	1.20850	0.604248	+	0.796796i	$0.293473\pi$
$390$	0	0
$391$	−2.83754	−0.143501
$392$	− 10.4218i	− 0.526380i
$393$	− 17.4504i	− 0.880258i
$394$	13.4135	0.675762
$395$	0	0
$396$	−5.42801	−0.272768
$397$	− 26.6992i	− 1.33999i	−0.742364	−	0.669997i	$-0.766295\pi$
$397$	− 26.6992i	− 1.33999i	0.742364	−	0.669997i	$-0.233705\pi$
$398$	9.31661i	0.467000i
$399$	2.59442	0.129883
$400$	0	0
$401$	21.8168	1.08948	0.544740	−	0.838605i	$-0.316628\pi$
$401$	21.8168	1.08948	0.544740	+	0.838605i	$0.316628\pi$
$402$	5.89296i	0.293914i
$403$	6.38880i	0.318249i
$404$	−28.4689	−1.41638
$405$	0	0
$406$	1.91595	0.0950869
$407$	− 11.4504i	− 0.567577i
$408$	− 3.89917i	− 0.193038i
$409$	1.16246	0.0574798	0.0287399	−	0.999587i	$-0.490851\pi$
$409$	1.16246	0.0574798	0.0287399	+	0.999587i	$0.490851\pi$
$410$	0	0
$411$	1.79834	0.0887055
$412$	− 16.2774i	− 0.801930i
$413$	− 8.45043i	− 0.415819i
$414$	0.874485	0.0429786
$415$	0	0
$416$	5.42801	0.266130
$417$	− 20.3249i	− 0.995315i
$418$	− 3.37202i	− 0.164931i
$419$	2.46326	0.120338	0.0601690	−	0.998188i	$-0.480836\pi$
$419$	2.46326	0.120338	0.0601690	+	0.998188i	$0.480836\pi$
$420$	0	0
$421$	27.6336	1.34678	0.673390	−	0.739287i	$-0.264837\pi$
$421$	27.6336	1.34678	0.673390	+	0.739287i	$0.264837\pi$
$422$	− 15.9322i	− 0.775565i
$423$	11.2633i	0.547640i
$424$	14.3210	0.695487
$425$	0	0
$426$	−5.61515	−0.272055
$427$	− 7.83923i	− 0.379367i
$428$	5.74106i	0.277505i
$429$	−3.24482	−0.156661
$430$	0	0
$431$	28.9114	1.39261	0.696307	−	0.717744i	$-0.254825\pi$
$431$	28.9114	1.39261	0.696307	+	0.717744i	$0.254825\pi$
$432$	− 2.14399i	− 0.103153i
$433$	− 13.7569i	− 0.661113i	−0.943786	−	0.330557i	$-0.892764\pi$
$433$	− 13.7569i	− 0.661113i	0.943786	−	0.330557i	$-0.107236\pi$
$434$	−5.21844	−0.250493
$435$	0	0
$436$	4.95289	0.237200
$437$	− 2.77761i	− 0.132871i
$438$	3.04711i	0.145596i
$439$	30.5081	1.45607	0.728036	−	0.685539i	$-0.240433\pi$
$439$	30.5081	1.45607	0.728036	+	0.685539i	$0.240433\pi$
$440$	0	0
$441$	−4.96080	−0.236228
$442$	− 1.06163i	− 0.0504965i
$443$	28.3064i	1.34488i	0.740152	+	0.672440i	$0.234754\pi$
$443$	28.3064i	1.34488i	−0.740152	+	0.672440i	$0.765246\pi$
$444$	5.90312	0.280150
$445$	0	0
$446$	6.38485	0.302331
$447$	17.1809i	0.812630i
$448$	− 1.68960i	− 0.0798262i
$449$	−0.769701	−0.0363244	−0.0181622	−	0.999835i	$-0.505782\pi$
$449$	−0.769701	−0.0363244	−0.0181622	+	0.999835i	$0.505782\pi$
$450$	0	0
$451$	−12.3849	−0.583180
$452$	− 15.9710i	− 0.751211i
$453$	3.99605i	0.187751i
$454$	−4.53940	−0.213045
$455$	0	0
$456$	3.81681	0.178739
$457$	− 15.0841i	− 0.705602i	−0.935698	−	0.352801i	$-0.885229\pi$
$457$	− 15.0841i	− 0.705602i	0.935698	−	0.352801i	$-0.114771\pi$
$458$	15.9921i	0.747261i
$459$	−1.85601	−0.0866313
$460$	0	0
$461$	10.3664	0.482810	0.241405	−	0.970424i	$-0.422392\pi$
$461$	10.3664	0.482810	0.241405	+	0.970424i	$0.422392\pi$
$462$	− 2.65040i	− 0.123308i
$463$	− 8.06389i	− 0.374761i	−0.982287	−	0.187380i	$-0.940000\pi$
$463$	− 8.06389i	− 0.374761i	0.982287	−	0.187380i	$-0.0599997\pi$
$464$	−5.02904	−0.233467
$465$	0	0
$466$	−0.654353	−0.0303123
$467$	− 30.8145i	− 1.42593i	−0.701201	−	0.712964i	$-0.747352\pi$
$467$	− 30.8145i	− 1.42593i	0.701201	−	0.712964i	$-0.252648\pi$
$468$	− 1.67282i	− 0.0773263i
$469$	14.7120	0.679338
$470$	0	0
$471$	7.67282	0.353545
$472$	− 12.4320i	− 0.572227i
$473$	32.5081i	1.49472i
$474$	1.69356	0.0777876
$475$	0	0
$476$	−4.43365	−0.203216
$477$	− 6.81681i	− 0.312120i
$478$	− 1.91595i	− 0.0876335i
$479$	−10.9938	−0.502319	−0.251159	−	0.967946i	$-0.580812\pi$
$479$	−10.9938	−0.502319	−0.251159	+	0.967946i	$0.580812\pi$
$480$	0	0
$481$	3.52884	0.160901
$482$	4.63136i	0.210953i
$483$	− 2.18319i	− 0.0993386i
$484$	−0.788172	−0.0358260
$485$	0	0
$486$	0.571993	0.0259461
$487$	− 29.3602i	− 1.33044i	−0.746649	−	0.665218i	$-0.768339\pi$
$487$	− 29.3602i	− 1.33044i	0.746649	−	0.665218i	$-0.231661\pi$
$488$	− 11.5328i	− 0.522065i
$489$	−0.471163	−0.0213067
$490$	0	0
$491$	−21.0577	−0.950320	−0.475160	−	0.879900i	$-0.657610\pi$
$491$	−21.0577	−0.950320	−0.475160	+	0.879900i	$0.657610\pi$
$492$	− 6.38485i	− 0.287851i
$493$	4.35355i	0.196074i
$494$	1.03920	0.0467560
$495$	0	0
$496$	13.6975	0.615036
$497$	14.0185i	0.628814i
$498$	1.79608i	0.0804842i
$499$	−23.8392	−1.06719	−0.533595	−	0.845740i	$-0.679159\pi$
$499$	−23.8392	−1.06719	−0.533595	+	0.845740i	$0.679159\pi$
$500$	0	0
$501$	−18.7098	−0.835891
$502$	14.5081i	0.647528i
$503$	− 21.8168i	− 0.972763i	−0.873746	−	0.486382i	$-0.838316\pi$
$503$	− 21.8168i	− 0.972763i	0.873746	−	0.486382i	$-0.161684\pi$
$504$	3.00000	0.133631
$505$	0	0
$506$	−2.83754	−0.126144
$507$	− 1.00000i	− 0.0444116i
$508$	0.306444i	0.0135963i
$509$	−2.01847	−0.0894672	−0.0447336	−	0.998999i	$-0.514244\pi$
$509$	−2.01847	−0.0894672	−0.0447336	+	0.998999i	$0.514244\pi$
$510$	0	0
$511$	7.60724	0.336525
$512$	− 20.6459i	− 0.912428i
$513$	− 1.81681i	− 0.0802141i
$514$	−11.2034	−0.494159
$515$	0	0
$516$	−16.7591	−0.737780
$517$	− 36.5473i	− 1.60735i
$518$	2.88239i	0.126645i
$519$	−7.96080	−0.349440
$520$	0	0
$521$	5.02073	0.219962	0.109981	−	0.993934i	$-0.464921\pi$
$521$	5.02073	0.219962	0.109981	+	0.993934i	$0.464921\pi$
$522$	− 1.34169i	− 0.0587244i
$523$	18.5266i	0.810111i	0.914292	+	0.405055i	$0.132748\pi$
$523$	18.5266i	0.810111i	−0.914292	+	0.405055i	$0.867252\pi$
$524$	−29.1915	−1.27524
$525$	0	0
$526$	−4.14625	−0.180785
$527$	− 11.8577i	− 0.516530i
$528$	6.95684i	0.302758i
$529$	20.6627	0.898376
$530$	0	0
$531$	−5.91764	−0.256804
$532$	− 4.34000i	− 0.188163i
$533$	− 3.81681i	− 0.165324i
$534$	2.77761	0.120199
$535$	0	0
$536$	21.6438	0.934869
$537$	− 15.6521i	− 0.675438i
$538$	− 8.29983i	− 0.357831i
$539$	16.0969	0.693342
$540$	0	0
$541$	7.61515	0.327401	0.163700	−	0.986510i	$-0.447657\pi$
$541$	7.61515	0.327401	0.163700	+	0.986510i	$0.447657\pi$
$542$	2.40106i	0.103134i
$543$	− 24.5658i	− 1.05422i
$544$	−10.0745	−0.431939
$545$	0	0
$546$	0.816810	0.0349563
$547$	17.9031i	0.765482i	0.923856	+	0.382741i	$0.125020\pi$
$547$	17.9031i	0.765482i	−0.923856	+	0.382741i	$0.874980\pi$
$548$	− 3.00830i	− 0.128508i
$549$	−5.48963	−0.234292
$550$	0	0
$551$	−4.26160	−0.181550
$552$	− 3.21183i	− 0.136704i
$553$	− 4.22804i	− 0.179794i
$554$	9.49794	0.403529
$555$	0	0
$556$	−34.0000	−1.44192
$557$	34.4218i	1.45850i	0.684248	+	0.729249i	$0.260130\pi$
$557$	34.4218i	1.45850i	−0.684248	+	0.729249i	$0.739870\pi$
$558$	3.65435i	0.154701i
$559$	−10.0185	−0.423736
$560$	0	0
$561$	6.02242	0.254267
$562$	− 13.9137i	− 0.586913i
$563$	41.5658i	1.75179i	0.482503	+	0.875894i	$0.339728\pi$
$563$	41.5658i	1.75179i	−0.482503	+	0.875894i	$0.660272\pi$
$564$	18.8415	0.793370
$565$	0	0
$566$	−4.41123	−0.185418
$567$	− 1.42801i	− 0.0599706i
$568$	20.6235i	0.865341i
$569$	26.0761	1.09317	0.546584	−	0.837404i	$-0.315928\pi$
$569$	26.0761	1.09317	0.546584	+	0.837404i	$0.315928\pi$
$570$	0	0
$571$	3.41349	0.142850	0.0714250	−	0.997446i	$-0.477245\pi$
$571$	3.41349	0.142850	0.0714250	+	0.997446i	$0.477245\pi$
$572$	5.42801i	0.226956i
$573$	− 21.0577i	− 0.879697i
$574$	3.11761	0.130127
$575$	0	0
$576$	−1.18319	−0.0492996
$577$	− 5.10704i	− 0.212609i	−0.994334	−	0.106305i	$-0.966098\pi$
$577$	− 5.10704i	− 0.212609i	0.994334	−	0.106305i	$-0.0339018\pi$
$578$	− 7.75349i	− 0.322503i
$579$	−19.9401	−0.828681
$580$	0	0
$581$	4.48399	0.186027
$582$	− 0.863919i	− 0.0358106i
$583$	22.1193i	0.916088i
$584$	11.1915	0.463107
$585$	0	0
$586$	3.43196	0.141773
$587$	20.8705i	0.861419i	0.902491	+	0.430710i	$0.141737\pi$
$587$	20.8705i	0.861419i	−0.902491	+	0.430710i	$0.858263\pi$
$588$	8.29854i	0.342226i
$589$	11.6072	0.478268
$590$	0	0
$591$	−23.4504	−0.964622
$592$	− 7.56578i	− 0.310952i
$593$	30.4403i	1.25003i	0.780612	+	0.625016i	$0.214908\pi$
$593$	30.4403i	1.25003i	−0.780612	+	0.625016i	$0.785092\pi$
$594$	−1.85601	−0.0761532
$595$	0	0
$596$	28.7407	1.17726
$597$	− 16.2880i	− 0.666622i
$598$	− 0.874485i	− 0.0357603i
$599$	−11.5658	−0.472565	−0.236282	−	0.971684i	$-0.575929\pi$
$599$	−11.5658	−0.472565	−0.236282	+	0.971684i	$0.575929\pi$
$600$	0	0
$601$	13.6728	0.557726	0.278863	−	0.960331i	$-0.410042\pi$
$601$	13.6728	0.557726	0.278863	+	0.960331i	$0.410042\pi$
$602$	− 8.18319i	− 0.333522i
$603$	− 10.3025i	− 0.419550i
$604$	6.68468	0.271996
$605$	0	0
$606$	−9.73445	−0.395435
$607$	− 15.4689i	− 0.627863i	−0.949446	−	0.313932i	$-0.898354\pi$
$607$	− 15.4689i	− 0.627863i	0.949446	−	0.313932i	$-0.101646\pi$
$608$	− 9.86166i	− 0.399943i
$609$	−3.34960	−0.135733
$610$	0	0
$611$	11.2633	0.455664
$612$	3.10478i	0.125503i
$613$	− 0.287973i	− 0.0116311i	−0.999983	−	0.00581556i	$-0.998149\pi$
$613$	− 0.287973i	− 0.0116311i	0.999983	−	0.00581556i	$-0.00185116\pi$
$614$	7.31475	0.295199
$615$	0	0
$616$	−9.73445	−0.392212
$617$	− 6.28007i	− 0.252826i	−0.991978	−	0.126413i	$-0.959654\pi$
$617$	− 6.28007i	− 0.252826i	0.991978	−	0.126413i	$-0.0403465\pi$
$618$	− 5.56578i	− 0.223888i
$619$	20.6314	0.829244	0.414622	−	0.909994i	$-0.363914\pi$
$619$	20.6314	0.829244	0.414622	+	0.909994i	$0.363914\pi$
$620$	0	0
$621$	−1.52884	−0.0613501
$622$	10.2959i	0.412827i
$623$	− 6.93442i	− 0.277822i
$624$	−2.14399	−0.0858282
$625$	0	0
$626$	7.94063	0.317372
$627$	5.89522i	0.235432i
$628$	− 12.8353i	− 0.512183i
$629$	−6.54957	−0.261148
$630$	0	0
$631$	−11.0392	−0.439464	−0.219732	−	0.975560i	$-0.570518\pi$
$631$	−11.0392	−0.439464	−0.219732	+	0.975560i	$0.570518\pi$
$632$	− 6.22013i	− 0.247424i
$633$	27.8538i	1.10709i
$634$	−4.58651	−0.182154
$635$	0	0
$636$	−11.4033	−0.452171
$637$	4.96080i	0.196554i
$638$	4.35355i	0.172359i
$639$	9.81681	0.388347
$640$	0	0
$641$	7.97136	0.314850	0.157425	−	0.987531i	$-0.449681\pi$
$641$	7.97136	0.314850	0.157425	+	0.987531i	$0.449681\pi$
$642$	1.96306i	0.0774757i
$643$	− 39.5658i	− 1.56032i	−0.625579	−	0.780161i	$-0.715137\pi$
$643$	− 39.5658i	− 1.56032i	0.625579	−	0.780161i	$-0.284863\pi$
$644$	−3.65209	−0.143913
$645$	0	0
$646$	−1.92878	−0.0758866
$647$	24.6992i	0.971026i	0.874230	+	0.485513i	$0.161367\pi$
$647$	24.6992i	0.971026i	−0.874230	+	0.485513i	$0.838633\pi$
$648$	− 2.10083i	− 0.0825284i
$649$	19.2017	0.753731
$650$	0	0
$651$	9.12325	0.357569
$652$	0.788172i	0.0308672i
$653$	37.7361i	1.47673i	0.674402	+	0.738365i	$0.264402\pi$
$653$	37.7361i	1.47673i	−0.674402	+	0.738365i	$0.735598\pi$
$654$	1.69356	0.0662233
$655$	0	0
$656$	−8.18319	−0.319500
$657$	− 5.32718i	− 0.207833i
$658$	9.19997i	0.358652i
$659$	49.6890	1.93561	0.967805	−	0.251701i	$-0.0809900\pi$
$659$	49.6890	1.93561	0.967805	+	0.251701i	$0.0809900\pi$
$660$	0	0
$661$	40.6235	1.58007	0.790035	−	0.613062i	$-0.210063\pi$
$661$	40.6235	1.58007	0.790035	+	0.613062i	$0.210063\pi$
$662$	19.5737i	0.760753i
$663$	1.85601i	0.0720816i
$664$	6.59668	0.256001
$665$	0	0
$666$	2.01847	0.0782142
$667$	3.58611i	0.138855i
$668$	31.2981i	1.21096i
$669$	−11.1625	−0.431566
$670$	0	0
$671$	17.8129	0.687658
$672$	− 7.75123i	− 0.299010i
$673$	− 17.7961i	− 0.685988i	−0.939338	−	0.342994i	$-0.888559\pi$
$673$	− 17.7961i	− 0.685988i	0.939338	−	0.342994i	$-0.111441\pi$
$674$	−12.2814	−0.473060
$675$	0	0
$676$	−1.67282	−0.0643394
$677$	24.8850i	0.956410i	0.878248	+	0.478205i	$0.158712\pi$
$677$	24.8850i	0.956410i	−0.878248	+	0.478205i	$0.841288\pi$
$678$	− 5.46100i	− 0.209728i
$679$	−2.15681	−0.0827709
$680$	0	0
$681$	7.93611	0.304112
$682$	− 11.8577i	− 0.454055i
$683$	− 27.3602i	− 1.04691i	−0.852054	−	0.523454i	$-0.824643\pi$
$683$	− 27.3602i	− 1.04691i	0.852054	−	0.523454i	$-0.175357\pi$
$684$	−3.03920	−0.116207
$685$	0	0
$686$	−9.76970	−0.373009
$687$	− 27.9585i	− 1.06668i
$688$	21.4795i	0.818897i
$689$	−6.81681	−0.259700
$690$	0	0
$691$	20.2919	0.771941	0.385971	−	0.922511i	$-0.373867\pi$
$691$	20.2919	0.771941	0.385971	+	0.922511i	$0.373867\pi$
$692$	13.3170i	0.506237i
$693$	4.63362i	0.176017i
$694$	15.2224	0.577834
$695$	0	0
$696$	−4.92781	−0.186788
$697$	7.08405i	0.268328i
$698$	− 7.90312i	− 0.299138i
$699$	1.14399	0.0432695
$700$	0	0
$701$	40.1888	1.51791	0.758956	−	0.651142i	$-0.225710\pi$
$701$	40.1888	1.51791	0.758956	+	0.651142i	$0.225710\pi$
$702$	− 0.571993i	− 0.0215885i
$703$	− 6.41123i	− 0.241804i
$704$	3.83923	0.144697
$705$	0	0
$706$	14.6023	0.549566
$707$	24.3025i	0.913989i
$708$	9.89917i	0.372034i
$709$	−20.9898	−0.788290	−0.394145	−	0.919048i	$-0.628959\pi$
$709$	−20.9898	−0.788290	−0.394145	+	0.919048i	$0.628959\pi$
$710$	0	0
$711$	−2.96080	−0.111039
$712$	− 10.2017i	− 0.382323i
$713$	− 9.76744i	− 0.365794i
$714$	−1.51601	−0.0567353
$715$	0	0
$716$	−26.1832	−0.978512
$717$	3.34960i	0.125093i
$718$	2.66452i	0.0994390i
$719$	−6.47907	−0.241628	−0.120814	−	0.992675i	$-0.538551\pi$
$719$	−6.47907	−0.241628	−0.120814	+	0.992675i	$0.538551\pi$
$720$	0	0
$721$	−13.8952	−0.517485
$722$	8.97984i	0.334195i
$723$	− 8.09688i	− 0.301126i
$724$	−41.0942	−1.52725
$725$	0	0
$726$	−0.269502	−0.0100022
$727$	22.7098i	0.842259i	0.907001	+	0.421129i	$0.138366\pi$
$727$	22.7098i	0.842259i	−0.907001	+	0.421129i	$0.861634\pi$
$728$	− 3.00000i	− 0.111187i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	18.5944	0.687739
$732$	9.18319i	0.339420i
$733$	− 43.0577i	− 1.59037i	−0.606366	−	0.795186i	$-0.707373\pi$
$733$	− 43.0577i	− 1.59037i	0.606366	−	0.795186i	$-0.292627\pi$
$734$	11.0207	0.406783
$735$	0	0
$736$	−8.29854	−0.305888
$737$	33.4297i	1.23140i
$738$	− 2.18319i	− 0.0803643i
$739$	38.4337	1.41380	0.706902	−	0.707311i	$-0.250092\pi$
$739$	38.4337	1.41380	0.706902	+	0.707311i	$0.250092\pi$
$740$	0	0
$741$	−1.81681	−0.0667422
$742$	− 5.56804i	− 0.204409i
$743$	18.2320i	0.668867i	0.942419	+	0.334433i	$0.108545\pi$
$743$	18.2320i	0.668867i	−0.942419	+	0.334433i	$0.891455\pi$
$744$	13.4218	0.492067
$745$	0	0
$746$	−3.50375	−0.128282
$747$	− 3.14003i	− 0.114888i
$748$	− 10.0745i	− 0.368359i
$749$	4.90086	0.179074
$750$	0	0
$751$	−25.3720	−0.925838	−0.462919	−	0.886401i	$-0.653198\pi$
$751$	−25.3720	−0.925838	−0.462919	+	0.886401i	$0.653198\pi$
$752$	− 24.1483i	− 0.880599i
$753$	− 25.3641i	− 0.924320i
$754$	−1.34169	−0.0488616
$755$	0	0
$756$	−2.38880	−0.0868799
$757$	32.1888i	1.16992i	0.811061	+	0.584962i	$0.198890\pi$
$757$	32.1888i	1.16992i	−0.811061	+	0.584962i	$0.801110\pi$
$758$	12.7614i	0.463515i
$759$	4.96080	0.180066
$760$	0	0
$761$	32.2280	1.16827	0.584133	−	0.811658i	$-0.301435\pi$
$761$	32.2280	1.16827	0.584133	+	0.811658i	$0.301435\pi$
$762$	0.104783i	0.00379590i
$763$	− 4.22804i	− 0.153065i
$764$	−35.2258	−1.27442
$765$	0	0
$766$	−21.2118	−0.766414
$767$	5.91764i	0.213674i
$768$	− 4.23030i	− 0.152648i
$769$	−39.5843	−1.42744	−0.713722	−	0.700429i	$-0.752992\pi$
$769$	−39.5843	−1.42744	−0.713722	+	0.700429i	$0.752992\pi$
$770$	0	0
$771$	19.5865	0.705391
$772$	33.3562i	1.20052i
$773$	− 19.4689i	− 0.700248i	−0.936703	−	0.350124i	$-0.886139\pi$
$773$	− 19.4689i	− 0.700248i	0.936703	−	0.350124i	$-0.113861\pi$
$774$	−5.73050	−0.205978
$775$	0	0
$776$	−3.17302	−0.113905
$777$	− 5.03920i	− 0.180780i
$778$	− 13.6336i	− 0.488789i
$779$	−6.93442	−0.248451
$780$	0	0
$781$	−31.8538	−1.13982
$782$	1.62306i	0.0580403i
$783$	2.34565i	0.0838266i
$784$	10.6359	0.379853
$785$	0	0
$786$	−9.98153	−0.356029
$787$	17.0722i	0.608558i	0.952583	+	0.304279i	$0.0984155\pi$
$787$	17.0722i	0.608558i	−0.952583	+	0.304279i	$0.901584\pi$
$788$	39.2284i	1.39746i
$789$	7.24877	0.258063
$790$	0	0
$791$	−13.6336	−0.484756
$792$	6.81681i	0.242225i
$793$	5.48963i	0.194943i
$794$	−15.2718	−0.541975
$795$	0	0
$796$	−27.2469	−0.965741
$797$	− 17.5187i	− 0.620543i	−0.950648	−	0.310272i	$-0.899580\pi$
$797$	− 17.5187i	− 0.620543i	0.950648	−	0.310272i	$-0.100420\pi$
$798$	− 1.48399i	− 0.0525326i
$799$	−20.9048	−0.739559
$800$	0	0
$801$	−4.85601	−0.171579
$802$	− 12.4791i	− 0.440651i
$803$	17.2857i	0.610000i
$804$	−17.2343	−0.607805
$805$	0	0
$806$	3.65435	0.128719
$807$	14.5104i	0.510789i
$808$	35.7529i	1.25778i
$809$	−16.2017	−0.569620	−0.284810	−	0.958584i	$-0.591931\pi$
$809$	−16.2017	−0.569620	−0.284810	+	0.958584i	$0.591931\pi$
$810$	0	0
$811$	21.5513	0.756767	0.378384	−	0.925649i	$-0.376480\pi$
$811$	21.5513	0.756767	0.378384	+	0.925649i	$0.376480\pi$
$812$	5.60329i	0.196637i
$813$	− 4.19771i	− 0.147220i
$814$	−6.54957	−0.229562
$815$	0	0
$816$	3.97927	0.139302
$817$	18.2017i	0.636796i
$818$	− 0.664918i	− 0.0232483i
$819$	−1.42801	−0.0498986
$820$	0	0
$821$	31.5288	1.10036	0.550182	−	0.835045i	$-0.314558\pi$
$821$	31.5288	1.10036	0.550182	+	0.835045i	$0.314558\pi$
$822$	− 1.02864i	− 0.0358779i
$823$	− 56.1971i	− 1.95891i	−0.201665	−	0.979455i	$-0.564635\pi$
$823$	− 56.1971i	− 1.95891i	0.201665	−	0.979455i	$-0.435365\pi$
$824$	−20.4421	−0.712135
$825$	0	0
$826$	−4.83359	−0.168182
$827$	51.5697i	1.79326i	0.442785	+	0.896628i	$0.353990\pi$
$827$	51.5697i	1.79326i	−0.442785	+	0.896628i	$0.646010\pi$
$828$	2.55748i	0.0888784i
$829$	14.0286	0.487235	0.243617	−	0.969871i	$-0.421666\pi$
$829$	14.0286	0.487235	0.243617	+	0.969871i	$0.421666\pi$
$830$	0	0
$831$	−16.6050	−0.576020
$832$	1.18319i	0.0410197i
$833$	− 9.20731i	− 0.319014i
$834$	−11.6257	−0.402566
$835$	0	0
$836$	9.86166	0.341073
$837$	− 6.38880i	− 0.220829i
$838$	− 1.40897i	− 0.0486719i
$839$	28.4712	0.982934	0.491467	−	0.870896i	$-0.336461\pi$
$839$	28.4712	0.982934	0.491467	+	0.870896i	$0.336461\pi$
$840$	0	0
$841$	−23.4979	−0.810274
$842$	− 15.8062i	− 0.544719i
$843$	24.3249i	0.837795i
$844$	46.5944	1.60385
$845$	0	0
$846$	6.44252	0.221499
$847$	0.672824i	0.0231185i
$848$	14.6151i	0.501886i
$849$	7.71203	0.264676
$850$	0	0
$851$	−5.39502	−0.184939
$852$	− 16.4218i	− 0.562601i
$853$	− 33.5552i	− 1.14891i	−0.818537	−	0.574454i	$-0.805214\pi$
$853$	− 33.5552i	− 1.14891i	0.818537	−	0.574454i	$-0.194786\pi$
$854$	−4.48399	−0.153439
$855$	0	0
$856$	7.20997	0.246432
$857$	− 37.8432i	− 1.29270i	−0.763042	−	0.646349i	$-0.776295\pi$
$857$	− 37.8432i	− 1.29270i	0.763042	−	0.646349i	$-0.223705\pi$
$858$	1.85601i	0.0633633i
$859$	−14.3849	−0.490805	−0.245402	−	0.969421i	$-0.578920\pi$
$859$	−14.3849	−0.490805	−0.245402	+	0.969421i	$0.578920\pi$
$860$	0	0
$861$	−5.45043	−0.185750
$862$	− 16.5371i	− 0.563257i
$863$	32.2610i	1.09818i	0.835764	+	0.549089i	$0.185025\pi$
$863$	32.2610i	1.09818i	−0.835764	+	0.549089i	$0.814975\pi$
$864$	−5.42801	−0.184665
$865$	0	0
$866$	−7.86884	−0.267394
$867$	13.5552i	0.460359i
$868$	− 15.2616i	− 0.518012i
$869$	9.60724	0.325903
$870$	0	0
$871$	−10.3025	−0.349087
$872$	− 6.22013i	− 0.210640i
$873$	1.51037i	0.0511181i
$874$	−1.58877	−0.0537410
$875$	0	0
$876$	−8.91143	−0.301089
$877$	− 57.6996i	− 1.94838i	−0.225736	−	0.974189i	$-0.572479\pi$
$877$	− 57.6996i	− 1.94838i	0.225736	−	0.974189i	$-0.427521\pi$
$878$	− 17.4504i	− 0.588924i
$879$	−6.00000	−0.202375
$880$	0	0
$881$	−56.6811	−1.90964	−0.954818	−	0.297192i	$-0.903950\pi$
$881$	−56.6811	−1.90964	−0.954818	+	0.297192i	$0.903950\pi$
$882$	2.83754i	0.0955450i
$883$	− 20.0863i	− 0.675958i	−0.941154	−	0.337979i	$-0.890257\pi$
$883$	− 20.0863i	− 0.675958i	0.941154	−	0.337979i	$-0.109743\pi$
$884$	3.10478	0.104425
$885$	0	0
$886$	16.1911	0.543950
$887$	17.2857i	0.580397i	0.956966	+	0.290199i	$0.0937214\pi$
$887$	17.2857i	0.580397i	−0.956966	+	0.290199i	$0.906279\pi$
$888$	− 7.41349i	− 0.248780i
$889$	0.261596	0.00877366
$890$	0	0
$891$	3.24482	0.108705
$892$	18.6728i	0.625212i
$893$	− 20.4633i	− 0.684777i
$894$	9.82738	0.328677
$895$	0	0
$896$	−16.4689	−0.550187
$897$	1.52884i	0.0510464i
$898$	0.440264i	0.0146918i
$899$	−14.9859	−0.499807
$900$	0	0
$901$	12.6521	0.421502
$902$	7.08405i	0.235873i
$903$	14.3064i	0.476089i
$904$	−20.0573	−0.667095
$905$	0	0
$906$	2.28571	0.0759377
$907$	48.4033i	1.60721i	0.595166	+	0.803603i	$0.297086\pi$
$907$	48.4033i	1.60721i	−0.595166	+	0.803603i	$0.702914\pi$
$908$	− 13.2757i	− 0.440570i
$909$	17.0185	0.564467
$910$	0	0
$911$	−9.16246	−0.303566	−0.151783	−	0.988414i	$-0.548501\pi$
$911$	−9.16246	−0.303566	−0.151783	+	0.988414i	$0.548501\pi$
$912$	3.89522i	0.128984i
$913$	10.1888i	0.337201i
$914$	−8.62798	−0.285388
$915$	0	0
$916$	−46.7697	−1.54531
$917$	24.9193i	0.822909i
$918$	1.06163i	0.0350389i
$919$	−7.06558	−0.233072	−0.116536	−	0.993186i	$-0.537179\pi$
$919$	−7.06558	−0.233072	−0.116536	+	0.993186i	$0.537179\pi$
$920$	0	0
$921$	−12.7882	−0.421385
$922$	− 5.92950i	− 0.195278i
$923$	− 9.81681i	− 0.323124i
$924$	7.75123	0.254997
$925$	0	0
$926$	−4.61249	−0.151576
$927$	9.73050i	0.319591i
$928$	12.7322i	0.417955i
$929$	−37.3042	−1.22391	−0.611955	−	0.790892i	$-0.709617\pi$
$929$	−37.3042	−1.22391	−0.611955	+	0.790892i	$0.709617\pi$
$930$	0	0
$931$	9.01283	0.295383
$932$	− 1.91369i	− 0.0626849i
$933$	− 18.0000i	− 0.589294i
$934$	−17.6257	−0.576731
$935$	0	0
$936$	−2.10083	−0.0686678
$937$	18.8353i	0.615322i	0.951496	+	0.307661i	$0.0995462\pi$
$937$	18.8353i	0.615322i	−0.951496	+	0.307661i	$0.900454\pi$
$938$	− 8.41518i	− 0.274765i
$939$	−13.8824	−0.453035
$940$	0	0
$941$	−53.6106	−1.74766	−0.873828	−	0.486235i	$-0.838370\pi$
$941$	−53.6106	−1.74766	−0.873828	+	0.486235i	$0.838370\pi$
$942$	− 4.38880i	− 0.142995i
$943$	5.83528i	0.190023i
$944$	12.6873	0.412938
$945$	0	0
$946$	18.5944	0.604557
$947$	12.6319i	0.410483i	0.978711	+	0.205241i	$0.0657979\pi$
$947$	12.6319i	0.410483i	−0.978711	+	0.205241i	$0.934202\pi$
$948$	4.95289i	0.160862i
$949$	−5.32718	−0.172927
$950$	0	0
$951$	8.01847	0.260017
$952$	5.56804i	0.180461i
$953$	58.8044i	1.90486i	0.304756	+	0.952430i	$0.401425\pi$
$953$	58.8044i	1.90486i	−0.304756	+	0.952430i	$0.598575\pi$
$954$	−3.89917	−0.126240
$955$	0	0
$956$	5.60329	0.181223
$957$	− 7.61120i	− 0.246035i
$958$	6.28837i	0.203168i
$959$	−2.56804	−0.0829263
$960$	0	0
$961$	9.81681	0.316671
$962$	− 2.01847i	− 0.0650781i
$963$	− 3.43196i	− 0.110593i
$964$	−13.5446	−0.436244
$965$	0	0
$966$	−1.24877	−0.0401785
$967$	6.43027i	0.206783i	0.994641	+	0.103392i	$0.0329695\pi$
$967$	6.43027i	0.206783i	−0.994641	+	0.103392i	$0.967030\pi$
$968$	0.989833i	0.0318144i
$969$	3.37202	0.108325
$970$	0	0
$971$	0.604983	0.0194148	0.00970741	−	0.999953i	$-0.496910\pi$
$971$	0.604983	0.0194148	0.00970741	+	0.999953i	$0.496910\pi$
$972$	1.67282i	0.0536558i
$973$	29.0241i	0.930470i
$974$	−16.7938	−0.538109
$975$	0	0
$976$	11.7697	0.376739
$977$	4.36638i	0.139693i	0.997558	+	0.0698464i	$0.0222509\pi$
$977$	4.36638i	0.139693i	−0.997558	+	0.0698464i	$0.977749\pi$
$978$	0.269502i	0.00861772i
$979$	15.7569	0.503592
$980$	0	0
$981$	−2.96080	−0.0945310
$982$	12.0448i	0.384367i
$983$	− 30.3025i	− 0.966499i	−0.875483	−	0.483250i	$-0.839456\pi$
$983$	− 30.3025i	− 0.966499i	0.875483	−	0.483250i	$-0.160544\pi$
$984$	−8.01847	−0.255620
$985$	0	0
$986$	2.49020	0.0793042
$987$	− 16.0841i	− 0.511961i
$988$	3.03920i	0.0966899i
$989$	15.3166	0.487040
$990$	0	0
$991$	−4.96870	−0.157836	−0.0789180	−	0.996881i	$-0.525147\pi$
$991$	−4.96870	−0.157836	−0.0789180	+	0.996881i	$0.525147\pi$
$992$	− 34.6785i	− 1.10104i
$993$	− 34.2201i	− 1.08594i
$994$	8.01847	0.254330
$995$	0	0
$996$	−5.25272	−0.166439
$997$	11.2959i	0.357744i	0.983872	+	0.178872i	$0.0572448\pi$
$997$	11.2959i	0.357744i	−0.983872	+	0.178872i	$0.942755\pi$
$998$	13.6359i	0.431636i
$999$	−3.52884	−0.111647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.c.j.274.3		6
3.2	odd	2		2925.2.c.x.2224.4		6
5.2	odd	4		975.2.a.p.1.2	yes	3
5.3	odd	4		975.2.a.n.1.2	✓	3
5.4	even	2	inner	975.2.c.j.274.4		6
15.2	even	4		2925.2.a.bg.1.2		3
15.8	even	4		2925.2.a.bi.1.2		3
15.14	odd	2		2925.2.c.x.2224.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.a.n.1.2	✓	3	5.3	odd	4
975.2.a.p.1.2	yes	3	5.2	odd	4
975.2.c.j.274.3		6	1.1	even	1	trivial
975.2.c.j.274.4		6	5.4	even	2	inner
2925.2.a.bg.1.2		3	15.2	even	4
2925.2.a.bi.1.2		3	15.8	even	4
2925.2.c.x.2224.3		6	15.14	odd	2
2925.2.c.x.2224.4		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.571993i q^{2} +1.00000i q^{3} +1.67282 q^{4} +0.571993 q^{6} -1.42801i q^{7} -2.10083i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.571993i q^{2} +1.00000i q^{3} +1.67282 q^{4} +0.571993 q^{6} -1.42801i q^{7} -2.10083i q^{8} -1.00000 q^{9} +3.24482 q^{11} +1.67282i q^{12} +1.00000i q^{13} -0.816810 q^{14} +2.14399 q^{16} -1.85601i q^{17} +0.571993i q^{18} +1.81681 q^{19} +1.42801 q^{21} -1.85601i q^{22} -1.52884i q^{23} +2.10083 q^{24} +0.571993 q^{26} -1.00000i q^{27} -2.38880i q^{28} -2.34565 q^{29} +6.38880 q^{31} -5.42801i q^{32} +3.24482i q^{33} -1.06163 q^{34} -1.67282 q^{36} -3.52884i q^{37} -1.03920i q^{38} -1.00000 q^{39} -3.81681 q^{41} -0.816810i q^{42} +10.0185i q^{43} +5.42801 q^{44} -0.874485 q^{46} -11.2633i q^{47} +2.14399i q^{48} +4.96080 q^{49} +1.85601 q^{51} +1.67282i q^{52} +6.81681i q^{53} -0.571993 q^{54} -3.00000 q^{56} +1.81681i q^{57} +1.34169i q^{58} +5.91764 q^{59} +5.48963 q^{61} -3.65435i q^{62} +1.42801i q^{63} +1.18319 q^{64} +1.85601 q^{66} +10.3025i q^{67} -3.10478i q^{68} +1.52884 q^{69} -9.81681 q^{71} +2.10083i q^{72} +5.32718i q^{73} -2.01847 q^{74} +3.03920 q^{76} -4.63362i q^{77} +0.571993i q^{78} +2.96080 q^{79} +1.00000 q^{81} +2.18319i q^{82} +3.14003i q^{83} +2.38880 q^{84} +5.73050 q^{86} -2.34565i q^{87} -6.81681i q^{88} +4.85601 q^{89} +1.42801 q^{91} -2.55748i q^{92} +6.38880i q^{93} -6.44252 q^{94} +5.42801 q^{96} -1.51037i q^{97} -2.83754i q^{98} -3.24482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 2 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 2 q^{6} - 6 q^{9} - 2 q^{11} + 18 q^{14} + 10 q^{16} - 12 q^{19} + 10 q^{21} - 6 q^{24} + 2 q^{26} + 26 q^{29} + 14 q^{31} + 38 q^{34} + 10 q^{36} - 6 q^{39} + 34 q^{44} + 52 q^{46} + 4 q^{49} + 14 q^{51} - 2 q^{54} - 18 q^{56} - 6 q^{59} - 10 q^{61} + 30 q^{64} + 14 q^{66} - 8 q^{69} - 36 q^{71} + 48 q^{74} + 44 q^{76} - 8 q^{79} + 6 q^{81} - 10 q^{84} - 20 q^{86} + 32 q^{89} + 10 q^{91} + 10 q^{94} + 34 q^{96} + 2 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^6 - 6 * q^9 - 2 * q^11 + 18 * q^14 + 10 * q^16 - 12 * q^19 + 10 * q^21 - 6 * q^24 + 2 * q^26 + 26 * q^29 + 14 * q^31 + 38 * q^34 + 10 * q^36 - 6 * q^39 + 34 * q^44 + 52 * q^46 + 4 * q^49 + 14 * q^51 - 2 * q^54 - 18 * q^56 - 6 * q^59 - 10 * q^61 + 30 * q^64 + 14 * q^66 - 8 * q^69 - 36 * q^71 + 48 * q^74 + 44 * q^76 - 8 * q^79 + 6 * q^81 - 10 * q^84 - 20 * q^86 + 32 * q^89 + 10 * q^91 + 10 * q^94 + 34 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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